Mathematics

Dr. Amey Deshpande
Pune University

Fractional calculus (FC) is witnessing rapid development in recent past. Due to its interdisciplinary nature, and applicability it has become an active area of research in various fields. Present talk deals with our work on fractional order dynamical systems (fractional systems).  We take an overview of local stable manifold theorem for fractional systems which asserts existence of a stable manifold in a neighborhood of an equilibrium point.  
  It has been established in the literature that fractional systems undergo bifurcations and exhibit chaos for different values of fractional order. Hence it is important to study bifurcations and chaos in fractional systems.  Hopf bifurcation is a type of local codimension 1 bifurcation exhibited by integer order dynamical systems.  We characterize fractional Hopf bifurcation and prove its existence in case of fractional Bhalekar-Gejji (BG) system. Further we also find  (global) threshold value of fractional order below which the chaos in the BG system disappears irrespective of values of its system parameters A and B.